Analytical Stiffness Optimization of High-Precision Hexapods for Large Optical Telescope Applications

An analytical stiffness and eigenfrequency model of symmetric parallel 6-6 Stewart platforms (hexapods) is developed based on geometrical design variables to optimize the dynamical performance. The model is based upon Lagrangean dynamics in which the Bryant angles are used for the kinematics formulation. With the analytical eigenfrequency model, optimum stiffness characteristics can be obtained for any industrial application with limited workspace such as optical collimation systems. The actuator length-flexibility dependency is also considered in the analytical model. It is proposed that to increase the actuation bandwidth in six degrees of freedom, an eigenfrequency cost function can be defined and optimized. (Less)